Abstract <p>The article presents a new approach to the construction of optimal algorithms for the localization of point signal sources that reveal themselves by generating ultrashort pulses at random moments of time and can be detected by them. The approach applies iterative course-of-values recursion to this class of problems. An analytically exact solution of the problem is found for the case when a priori probability density of the source sought is given by a piecewise constant function of arbitrary complexity. The entire process of constructing an optimal search algorithm minimizing the mathematical expectation of the total localization time of the pulsed point source sought is fully formalized and implemented as an autonomous software module</p>